Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution

Thuto Mothupi; Wilson Moseki Thupeng; Baitshephi Mashabe; Botho Mokoto

doi:doi:10.11648/j.ajtas.20160506.16

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Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution

Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)

Received: 10 October 2016 Accepted: 22 October 2016 Published: 14 November 2016

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Abstract

In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)
DOI	10.11648/j.ajtas.20160506.16
Page(s)	365-375
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Maximum Temperature, Extreme Value, Return Level, Generalized Extreme Value Distribution, Stationarity, Climate Change

References

[1]	Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain ‘goodness-of-ﬁt’ criteria based on stochastic processes. The Annals of Mathematical Statistics, vol. 23, No. 2, 193-212.
[2]	Arreyndip NA, Joseph E (2015) Extreme temperature forecast in Mbonge, Cameroon, through return level analysis of the generalized extreme value (GEV) distribution. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering vol. 9, No. 6, 343–348.
[3]	Bandyopadhyay, N., Bhuiyan, C., and Saha, A. K. (2016), Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, vol. 82, issue 1, 367-388.
[4]	Barriopedro, D., Fischer, E. M., Luterbacher, J., Trigo, R. M., and Garcia-Herrera, R. (2011). The hot summer of 2012: Redrawing the temperature record map of Europe, Science 332 (6026), 220-224.
[5]	Beirlant, J., Goegebeur, Y., Segers, J. and Teugels, J. (2004). Statistics of extremes. Theory and Applications, with contributions from de Waal, D. J. and Ferro, C. Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester.
[6]	Bhuiyan, C. (2008). Desert Vegetation during Droughts: Response and Sensitivity. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B8. Beijing.
[7]	Bouza-Deano, R., Ternero-Rodriguez, M., and Fernandez-Espinosa, A. J. (2008). Trend study and assessment of surface water quality in the Ebro River (Spain). Journal of Hydrology 361, 227–239.
[8]	Byakatonda, J., Parida, P. B., and Kenabatho, K. P. (2015). Climate Variability and Trends in Meteorological Time Series in Semi-Arid Botswana. 10th Alexander von Humboldt International Conference. Addis Ababa (Ethiopia) 18–20 November 2015, AvH10-54.
[9]	Chikobvu, D. and Sigauke, C. (2013). Modelling influence of temperature on daily peak electricity demand in South Africa. Journal of Energy in South Africa 24(4), 63-70.
[10]	Coles, S. (2001). An introduction to Statistical Modelling of Extreme Values. Springer-Verlag, London.
[11]	Dai, K., Trenberth, K., and Qian, T. (2004). A Global Dataset of Palmer Drought Severity Index for 1870-2002: Relationship with Soil Moisture and Surface Warming. Journal of Hydrometeorology 5 (6), 1117-1130.
[12]	de Haan, L. and Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer Series in Operations Research and Financial Engineering.
[13]	Ebi, K. L. and Bowen, K. (2016). Extreme events as sources of health vulnerability: Drought as an example. Weather and Climate Extremes 11 (2016), 95-102.
[14]	Fischer, E. M. and Schär, C. (2010). Consistent geographical patterns of changes in high-impact European heatwaves. Nature Geoscience 3, 398–403.
[15]	Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society 24,180–190.
[16]	Fuentes, M., Henry, J., and Reich, B. (2013). Nonparametric Spatial Models for Extremes: Application to Extreme Temperature Data. Extremes 16, 75-101.
[17]	Gilbert, R. O. (1987). Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold Company Inc., New York.
[18]	Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’unesériealéatoire. Annals of Mathematics 44, 423–453.
[19]	Hasan, H. B., Ahmad Radi, N. F. B. and Kassim, S. B. (2012). Modelling of Extreme Temperature Using Generalized Extreme Value (GEV) Distribution: A Case Study of Penang. World Congress on Engineering 2012. Vol. 1, 181-186.
[20]	Helsel, D. R. and R. M. Hirsch. (2002). Statistical methods in water resources. Studies in Environmental Science 49. New York: Elsevier. (available on-line as a pdf file at: http://water.usgs.gov/pubs/twri/twri4a3/) Accessed 4-10-2016.
[21]	Hirsch, R. M., Slack, J. R, and Smith, R. A. (1982). Techniques of trend analysis for monthly water quality data. Water Resources. Research 18, 107-121.
[22]	Hirsch, R. M. and J. R. Slack. (1984). A nonparametric trend test for seasonal data with serial dependence. Water Resources Research 20 (6):727-732.
[23]	Hosking, J. R. M. (1985). Algorithm AS 215: Maximum-likelihood estimation of the parameter of the generalized extreme-value distribution. Applied Statistics 34, 301–310.
[24]	IPCC (2007). Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B, Tignor, M. and Miller, H. L. (editors). Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 996 pp.
[25]	IPCC (2013): Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T. F., D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P. M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 1535 pp.
[26]	Jenkins, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological events. Quarterly Journal of the Royal Meteorological Society 81, 158-172.
[27]	Kwiatkowski, D., Phillips, P. C. B., and Shin, P. S., Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159-178. North-Holland.
[28]	Katz, R., Parlange, M. B., and Naveau, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources 25, 12871304.
[29]	Kendall, M. G. (1975). Rank correlation methods, 4th ed. Charles Griffin, London.
[30]	Leadbetter, M. R., Lindgreen, G., and Rootzen, H. (1983). Extremes and Related Properties of Random Sequences and Series. Springer-Verlag, New York.
[31]	MacLeod, A. J. (1989). AS R76 - A remark on algorithm AS 215: Maximum likelihood estimation of the parameters of the generalized extreme value distribution. Applied Statistics 38 (3), 198–199.
[32]	Mann, H. B. (1945). Non-parametric tests against trend. Econometrica 13,163-171.
[33]	Marsaglia, G. and Marsaglia, J. (2004) Evaluating the Anderson-Darling Distribution. Journal of Statistical Software 9 (2), 1–5. http://www.jstatsoft.org/v09/i02. Accessed 04-10-2016.
[34]	Meehl, G. A., and C. Tebaldi (2004). More intense, more frequent, and longer lasting heat waves in the 21st century. Science 305, 994–997.
[35]	Parida, B. P., Moalafhi, D. B., Dube, O. P. (2005). Estimation of Likely Impact of Climate variability on Runoff Coefficients from Limpopo Basin using Artificial Neural Networks (ANN). In: Proceedings of the International Conference on Monitoring, Prediction and Mitigation of Water-Related Disasters, 12–15 January, Kyoto University, Japan, pp. 443–449.
[36]	Parida, B. P. and Moalafhi D. B. (2008), Regional rainfall frequency analysis for Botswana using L-Moments and radial basis function network. Physics and Chemistry of the Earth, Parts A/B/C, 33(8), 614-620.
[37]	Parey, S., Hoang, T. T. H., Dacunha-Castelle (2013). The importance of mean and variance in predicting changes in temperature extremes. Journal of Geophysical Research: Atmospheres 118, 8285–8296.
[38]	Raskin, P. and Kemp-Benedict, E. (2004). Background Paper for UNEP’s Third Global Environment Outlook Report (GEO-3), UNEP, Kenya.
[39]	Ray, K., Mohapatra, M., Bandyopadhyay, B. K., and Rathore, L. S. (Editors) (2015). High-Impact Weather Events over the SAARC Region. Springer Heidelberg New York Dordrecht London.
[40]	Shaby, B. A. and Reich, B. J. (2012). Bayesian spatial extreme value analysis to assess the changing risk of concurrent high temperatures across large portions of European cropland. Environmetrics 23, 638–648.
[41]	Siliverstovs, B., Oetsch, R., Kemfert, C., Jaeger, C., Haas, A., and Kremers, H. (2008). Climate Change and Modelling of Extreme Temperatures in Switzerland. DIW Berlin Discussion Paper No 840.
[42]	Stephenson, A. and Tawn, J. (2004). Bayesian inference for extremes: accounting for the three extremal types. Extremes 7, 291-307.
[43]	Thupeng, W. M. and Kgosi, P. M. (2012). The Deviance Information Criterion as a Bayesian Measure of Model Assessment for Extreme Values. Pioneer Journal of Theoretical and Applied Statistics Volume 3, Issue 2, 93-103.
[44]	United Nations Framework Convention on Climate Change (UFCCC) (2016). https://en.wikipedia.org/wiki/Paris_Agreement. Accessed 19 May 2016.
[45]	Van Den Brink, H. W., Konnen, G. P, Opsteegh, J. D., Van Oldenborgh, G. J., and Burgers, G. (2005): Estimating return periods of extreme events from ECMWF seasonal forecast ensembles. International Journal of Climatology 25, 1345–1354.
[46]	Wang, W., Van Gelder, G. P. and Vrijling, J. K. (2005). Trend and Stationary Analysis for Streamflow Processes of Rivers in Western Europe in the 20th Century. IWA International Conference on Water Economics, Statistics and Finance, Rethymno, Greece.
[47]	Wang, W., Vrijling, J. K., Van Gelder, P. H. A. J. M., and Ma, J (2006) Testing for nonlinearity of stream flow processes at different timescales. Journal of Hydrology, 322 (1–4), 247–268.
[48]	Wen, Fang, Qi, Zhou and Gao (2015). Changes of temperature and precipitation extremes in China: past and future. Theoretical and Applied Climatology, 10.1007/s00704-015-1584-x, 369-383.
[49]	Yilmaz, A. G. and Perera, B. J. C. (2014). Extreme Rainfall Nonstationary Investigation and Intensity-Frequency-Duration Relationship. Journal of Hydrologic Engineering, Vol. 19, No. 6, 1160-1172.
[50]	Yoo, S-H. (2007). Urban Water Consumption and Regional Economic Growth: The Case of Taejeon, Korea. Water Resources Management 21, 1353–1361.

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APA Style

Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto. (2016). Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. American Journal of Theoretical and Applied Statistics, 5(6), 365-375. https://doi.org/10.11648/j.ajtas.20160506.16

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ACS Style

Thuto Mothupi; Wilson Moseki Thupeng; Baitshephi Mashabe; Botho Mokoto. Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. Am. J. Theor. Appl. Stat. 2016, 5(6), 365-375. doi: 10.11648/j.ajtas.20160506.16

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AMA Style

Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto. Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. Am J Theor Appl Stat. 2016;5(6):365-375. doi: 10.11648/j.ajtas.20160506.16

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@article{10.11648/j.ajtas.20160506.16,
  author = {Thuto Mothupi and Wilson Moseki Thupeng and Baitshephi Mashabe and Botho Mokoto},
  title = {Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {365-375},
  doi = {10.11648/j.ajtas.20160506.16},
  url = {https://doi.org/10.11648/j.ajtas.20160506.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.16},
  abstract = {In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.},
 year = {2016}
}

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TY  - JOUR
T1  - Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution
AU  - Thuto Mothupi
AU  - Wilson Moseki Thupeng
AU  - Baitshephi Mashabe
AU  - Botho Mokoto
Y1  - 2016/11/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.16
DO  - 10.11648/j.ajtas.20160506.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 365
EP  - 375
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.16
AB  - In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.
VL  - 5
IS  - 6
ER  -

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Author Information

Thuto Mothupi

Department of Statistics, University of Botswana, Gaborone, Botswana
Wilson Moseki Thupeng

Department of Statistics, University of Botswana, Gaborone, Botswana
Baitshephi Mashabe

Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
Botho Mokoto

Department of Risk Management, Insurance and Actuarial Science, Ba Isago University, Gaborone, Botswana

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Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto. (2016). Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. American Journal of Theoretical and Applied Statistics, 5(6), 365-375. https://doi.org/10.11648/j.ajtas.20160506.16

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ACS Style

Thuto Mothupi; Wilson Moseki Thupeng; Baitshephi Mashabe; Botho Mokoto. Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. Am. J. Theor. Appl. Stat. 2016, 5(6), 365-375. doi: 10.11648/j.ajtas.20160506.16

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AMA Style

Thuto Mothupi, Wilson Moseki Thupeng, Baitshephi Mashabe, Botho Mokoto. Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution. Am J Theor Appl Stat. 2016;5(6):365-375. doi: 10.11648/j.ajtas.20160506.16

Copy | Download

@article{10.11648/j.ajtas.20160506.16,
  author = {Thuto Mothupi and Wilson Moseki Thupeng and Baitshephi Mashabe and Botho Mokoto},
  title = {Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {365-375},
  doi = {10.11648/j.ajtas.20160506.16},
  url = {https://doi.org/10.11648/j.ajtas.20160506.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.16},
  abstract = {In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Estimating Extreme Quantiles of the Maximum Surface Air Temperatures for the Sir Seretse Khama International Airport Using the Generalized Extreme Value Distribution
AU  - Thuto Mothupi
AU  - Wilson Moseki Thupeng
AU  - Baitshephi Mashabe
AU  - Botho Mokoto
Y1  - 2016/11/14
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.16
DO  - 10.11648/j.ajtas.20160506.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 365
EP  - 375
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.16
AB  - In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.
VL  - 5
IS  - 6
ER  -

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